How do astronomers calculate the expansion of the universe?
The red shift.
In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum. This happens when light emitting galaxies move away from us. To date, astronomers have found galaxies at about 13 billion light years distant. And they know that galaxies were not formed for at least the first 500 million years.
They have found that the more distant the galaxy, the faster it is moving away from us. For this they use Hubble's Constant - H0 ~ (30 km/s)/Million light years. And from this, we know that the universe is expanding, although the exact rate is unknown. Some postulate that it me be at or greater than the speed of light.